For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
08/04/2009

PROBLEM # 1
A confused bank teller transposed the dollars and cents when he cashed a check for Ms Smith, giving her dollars instead of cents and cents instead of dollars. After buying a newspaper for 50 cents, Ms Smith noticed that she had left exactly three times as much as the original check. What was the amount of the check?

PROBLEM #2
What is the minimum number of times a fair die must be thrown for there to be at least an even chance that all scores appear at least once?

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Problem Solutions 07/23/09

PROBLEM # 1

Using a balance scale and four weights you must be able to balance any integer load from 1 to 40. How much should each of the four weights weigh?

Solution:

PROBLEM #2

A circle whose center is (1,r) is tangent to x-axis and to the curve y = x^2 in the first quadrant. Determine r to the nearest hundredth.

Solution:

Congratulations to Shirish Dave, Shailesh Goregaokar and Ranganath Nayak, who were the winner of the last set of puzzles.

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